308 Mr. F. Y. Edge worth on the Law of Error 



Alcohol : — 



Ether :— 

 Mercury : — 



Carbonic acid : — 



log^ = 7-448 - 1 y W ' 



i a qqpq 3047 



logp = 6-9968-- I : I5 3 



log^^^esi- 5 ^ 5 . 



log^=8-4625-^|* 



XLIII. The Law of Error and the Elimination of Chance. By 

 F. Y. Edgeworth, M.A., Lecturer on Logic, King's 

 College, London* 



ONE of the principal uses of the Law of Error is to elimi- 

 nate chance in cases like the following. The mean (or 

 sum) of a set of observations t differs by a certain extent 

 from an assigned value \ ; usually that value which, upon 

 the supposition that no disturbing cause other than chance 

 had been at work, would be most likely to occur. It is 

 required to determine the probability that the observed 

 divergence is due to a disturbing cause rather than mere 

 chance. The general method may be summarized as follows. 

 Let x be the extent of observed divergence from the value 

 most probable on the supposition of mere chance. The pro- 

 bability of this amount of divergence in an assigned direction 

 (positive or negative) occurring by mere chance is approxi- 

 mately 



1 -I 2 7 

 e c2 doc, 



. 



• 



ire 



where c is a constant depending upon the number and cha- 

 racter of the observations. To which is to be added a certain 

 term outside the sign of integration, when we are dealing with 

 discrete errors, as in Bernouilli's theorem, rather than with 

 continuous quantity, as in the ordinary theory of errors of 



* Communicated by the Author. 



t Or more generally elements subject to definite laws of facility; such 

 as those which Mr. Galton supposes to obey individually the simplest 

 binomial law, and by their composition to constitute an approximate 

 probability-curve, such as we find in rerum naturd (Phil. Mag. Jan. 1875). 



% Whether a fixed quantity or the mean (or sum) of another set of 

 observations (or more generally elements). 



